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How to graph these curves?

  1. Nov 16, 2004 #1

    I was wondering how would I graph a sketch of these curves without knowing any values of them? They are orthogonal trajectories btw

    i) x^2 + y^2 = ax
    x^2 + y^2 = by

    ii) y = ax^3
    x^2 + 3y^2 = b

    Thanks in advnace.
  2. jcsd
  3. Nov 17, 2004 #2


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    x2+ y2= ax is the same as

    x2- ax+ y2= 0. Now complete the square in the x variable:

    x2- ax+ a2/4+ y2= a2/4
    (x- a/2)2+ y2= a2/2.

    That's a circle with center at (a/2, 0) and radius a/2 (so it goes through (0,0)).

    x2 + y2 = by

    Same thing: a circle with center at (0, b/2) and radius b/2 (and goes through (0,0)).

    y = ax3
    Well, that's just a pretty standard cubic. Goes through(-2,-8a), (-1, -a), (0,0), (1, a), (2, 8a), etc.

    x2 + 3y2 = b
    Same as x2/b + y2/(b/3)= 1,
    an ellipse with center at (0,0) vertices (√(b), 0), (-&radic(b),0), (0, √(b/3)), (0,-√(b/3)).
  4. Nov 17, 2004 #3
    Thanks a lot man. Really appreciate it.
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